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g(x)= l2xl +2

find domain and range

Gx L2xl 2 Find Domain And Range class=

Sagot :

The domain of the function g(x)=l2xl +2 is all real numbers and the range is from (0,∞).

Given g(x)= l2xl +2

First of all we know that modulas gives two values for x<0 and x>=0.

The function g(x) if opened gives two values.

for x>=0 g(x)=2x+2

for x<0 g(x)=-2x+2

because we have not told about the description about x so we can put any value in the function.

So the domain is all real numbers.

Now when we take g(x)=2x+2 for x>=0

putting x=0 we get 2 and rest are positive values so the value of g(x) keeps increasing as we increase the value of x. So here range is [2,∞).

Now take g(x)=-2x+2 for x<0

putting smallest number starting from zero but not 0 we will get a number near to 0 but not zero and because when a negative number multiplies with -2 it becomes positive and increase the value of g(x) so here the range becomes (0,∞).

When we talk about overall range it will be [2,∞) ∪(0,∞)

it will be (0,∞).

Hence the domain of the function g(x) is all real numbers and range is from 0 to infinity.

Learn more about domain and range at https://brainly.com/question/2264373

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